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On λ-invariants of number fields and étale cohomology

Published online by Cambridge University Press:  05 July 2013

Manfred Kolster  and
Abbas Movahhedi
Manfred Kolster
Affiliation:
Department of Mathematics, McMaster University, 1280 Main St. West Hamilton, Ontario L8S 4K1, Canadakolster@mcmaster.ca
Abbas Movahhedi
Affiliation:
Université de Limoges, XLIM UMR 7252 CNRS, 123 Av. Albert Thomas, 87060 Limoges Cedex, Francemova@unilim.fr
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Abstract

For an odd prime p we prove a Riemann-Hurwitz type formula for odd eigenspaces of the standard Iwasawa modules over F(μp∞), the field obtained from a totally real number field F by adjoining all p-power roots of unity. We use a new approach based on the relationship between eigenspaces and étale cohomology groups over the cyclotomic ℤp-extension F∞ of F. The systematic use of étale cohomology greatly simplifies the proof and allows to generalize the classical result about the minus-eigenspace to all odd eigenspaces.

Keywords

Iwasawa theoryétale cohomologyλ-invariants11R2311R3419F27

Information

Type
Research Article
Information
Journal of K-Theory , Volume 12 , Issue 1: Nanjing Special Issue on K-theory, number theory and geometry , August 2013 , pp. 167 - 181
Copyright
Copyright © ISOPP 2013 

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